SilentP, it souldn't be necessary to see the alien species' planet in order to confirm the the aliens' existence.
Listening for their EM communications should be more than enough. We listened since the 1960s - and so far, nothing. The stars are strangely quiet.

Here's your first problem, we've only been listening since the 1960s. That means we've only listened up to 40~50 lightyears away from ourselves. It also assumes that even if something has been transmitted in our direction in the correct timeframe that the signal even has the correct strength to even register on any particular sensor we care to use.

To be fair - most EM signals we have so far emitted should be incomprehensible to any alien astronomer (due to interference from the sun). But the carrier wave could be identified as being artificial. And, of course, we should be listening to EM signals from civilizations much more advanced than our own - the assumtion being that a more efficient/undetectable for us means for transmitting information (faster than light, that is) does not exist (according to relativity, such a thing can't exist).

See above point about signal degradation and dissappearing.

Also, here lies the assumption that the species in question doesn't have some form of communication that isn't FTL. I'd throw out the example of the theoratical method using a 'split' particle and changing the spin on one halfs, which the other half responds to by spinning the other way. Anyone know what it is I'm thinking of?

Also, it may be possible that a form of FTL travel exists, but no capability for signals to do the same with pure EM signals, hence some kind of messenger craft being used instead.

Admittedly the previous two points are purely hypothetical, but then again, we can't assume that aliens haven't found ways around hurdles that we struggle with.

Another way to confirm the existance of alien spacefaring species is to detect one of their vessels/probes - at present, this is possible only if said probe is near/in our solar system. If these aliens use Von Neumann probes to explore the galaxy, the probability of a Von Neumann probe reaching our solar system is significant - a Von Neumann probe is a robot that multiplies itself when it reaches a solar system/a place with prime materials, energy; the newly constructed probes are sent to other systems where they will multiply etc; in other words, their numbers increase exponentially.

This cannot be argued, though as you admit, this is incredibly difficult to detect. As we've seen with even detecting planetoids in our own system, it's very difficult to keep a track of all the objects within our solar system. However, emissions from a vessel within our space would dramatically increase the chances of such detection.

About Purple Buddha's analogy - imagine there are millions of cats in the forest (as my expansion of the analogy indicates should be).
What is the chance of one stumbling onto another - blind or not? In my opinion, there is a really good chance of such a thing happening frequently.

Problem here being we don't know, since we've never tried to pull off any experiment close to this, though one could try and have a computer model try to emulate the possibilities. However, since any chaotic system is quite dependent upon initial variables (of which in this case, we have little knowledge), the whole thing can be thrown into unexpected avenues of results.